Search results for "Ritz method"
showing 10 items of 18 documents
Buckling and post-buckling analysis of cracked stiffened panels via an X-Ritz method
2019
Abstract A multi-domain eXtended Ritz formulation, called X-Ritz, for the analysis of buckling and post-buckling of stiffened panels with cracks is presented. The theoretical framework is based on the First-order Shear Deformation Theory and accounts for von Karman's geometric nonlinearities. The structure is modeled as assembly of plate elements. Penalty techniques are used to fulfill the continuity condition along the edges of contiguous elements and to satisfy essential boundary conditions requirements. The use of an extended set of approximating functions allows to model through-the-thickness cracks and to capture the crack opening and tip singular fields as well as the structural behav…
Ritz Model for Damage Analysis in Variable Angle Tow Composite Plates
2022
In this work, a Ritz method is developed for progressive damage analysis of multilayered variable angle tow (VAT) composite plates under geometrically non-linear strains. The proposed model adopts a first order shear deformation theory and considers geometric non-linearities through the von Karman assumptions. A meso-modelling approach based on Continuum Damage Mechanics is adopted for analysing the initiation and evolution of damage. The onset of damage is predicted using the Hashin’s criteria. Four damage indices are defined and computed for expressing the degradation of the mechanical properties of the material, both for fibers and matrix under either tension and compression loading. A s…
Convergence of Boobnov-Galerkin Method Exemplified
2004
In this Note, Boobnov–Galerkin’s method is proved to converge to an exact solution for an applied mechanics problem. We address in detail the interrelation of Boobnov–Galerkin method and the exact solution in the beam deflection problems. Namely, we show the coincidence of these two methods for clamped–clamped boundary conditions, using an alternative set of functions proposed by Filonenko-Borodich.12 Received 25 February 2003; accepted for publication 13 March 2004. Copyright c 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to th…
A non-linear Ritz method for progressive failure analysis of variable angle tow composite laminates
2022
A Ritz formulation for non-linear analysis of damage initiation and evolution in variable angle tow composite plates under progressive loading is presented. The model is built on a few key items. It assumes first order shear deformation theory kinematics and non-liner strains in the von Karman sense. The constitutive relationships are formulated in the framework of continuum damage mechanics at the ply level, so that each laminate layer can experience in-plane damage initiation and evolution, then reflected in material softening and loss of local stiffness. A Ritz polynomial expansion of the primary variables and the minimization of the total potential energy provide the discrete solution e…
An extended Ritz formulation for buckling and post-buckling analysis of cracked multilayered plates
2018
Abstract An extended Ritz formulation for the analysis of buckling and post-buckling behaviour of cracked composite multilayered plates is presented. The formulation is based on: (i) the First-order Shear Deformation Theory to model the mechanics of the multilayered plate; (ii) the von Karman’s theory to account for geometric non-linearities ; (iii) the use of an extended set of approximating functions able to model the presence of an embedded or edge crack and to capture the crack opening fields as well as the global behaviour within a single cracked domain. The numerical results of the buckling analyses and the equilibrium paths in the post-buckling regime are compared with the results fr…
X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks
2019
The analysis of large amplitude vibrations of cracked plates is considered in this study. The problem is addressed via a Ritz approach based on the first-order shear deformation theory and von Karman’s geometric nonlinearity assumptions. The trial functions are built as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour (which motivates why the method is dubbed as eXtended Ritz); boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions along the plate edges. Convergence and accuracy are assessed to validate the approach and show its efficiency and potential. Original results are then…
A Rayleigh-Ritz approach for postbuckling analysis of variable angle tow composite stiffened panels
2018
Abstract A Rayleigh-Ritz solution approach for generally restrained multilayered variable angle tow stiffened plates in postbuckling regime is presented. The plate model is based on the first order shear deformation theory and accounts for geometrical nonlinearity through the von Karman’s assumptions. Stiffened plates are modelled as assembly of plate-like elements and penalty techniques are used to join the elements in the assembled structure and to apply the kinematical boundary conditions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed to build the trial functions. A computer code was developed to implement the propose…
Post-buckling analysis of cracked multilayered composite plates by pb-2 Rayleigh–Ritz method
2015
Abstract A pb-2 Rayleigh–Ritz variational approach for the analysis of post-buckling behavior of cracked composite plates is presented. The plate is modeled by the first order shear deformation theory taking geometric nonlinearities into account through the von Karman’s theory. General stacking sequences are considered. Cracks are modeled by using subdomain decomposition of the plate coupled with penalty techniques, used to augment the variational statement with the needed continuity conditions along the connected subdomains edges. Numerical procedures have been developed and used to validate the present solution by comparison with available literature results. Original results are then pre…
Post-Buckling Analysis of Damaged Multilayered Composite Stiffened Plates by Rayleigh-Ritz Method
2016
A Rayleigh-Ritz approach for the analysis of buckling and post-buckling behavior of cracked composite stiffened plates is presented. The structure is modeled as the assembly of plate elements modeled by the first order shear deformation theory and taking geometric nonlinearities into account through the von Karman’s theory assumptions. Continuity along the plate elements connected edges and the enforcement of rigid and elastic restraints of the plate boundaries are obtained by using penalty techniques, which also allow to straightforwardly implement efficient crack modeling strategies. General symmetric and unsymmetric stacking sequences are considered and numerical procedures have been dev…
A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates
2019
Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman’s geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thicknes…